A PRELIMINARY DESIGN METHODOLOGY FOR FATIGUE LIFE PREDICTION OF
POLYMER COMPOSITES FOR TIDAL TURBINE BLADES
Ciaran R. Kennedy
Mechanical and Biomedical
Engineering, NUI Galway,
Ireland
Sean B. Leen
Mechanical and Biomedical
Engineering, NUI Galway,
Ireland
Conchúr M. Ó Brádaigh
Mechanical and Biomedical
Engineering, NUI Galway,
Ireland
ABSTRACT
This paper is concerned with the development of a fatigue life prediction methodology for preliminary
design of polymer composites for ocean energy structures. To this end, a programme of fatigue testing of glass
fibre reinforced laminates is employed to characterise the strain-life behaviour of two candidate material
combinations. The test specimens are made from quasi-isotropic laminates of both vinyl-ester and epoxy
matrices. A preliminary finite element model of a tidal turbine blade is developed to identify the relevant
stresses and strains under representative hydrodynamic loading. The hydrodynamic (blade) loads are calculated
using a stream tube momentum model, based on tidal current velocities predicted by a sinusoidal equation. The
comparative fatigue behaviour of the candidate materials is assessed in the context of the turbine blade model.
1. INTRODUCTION
The emerging field of ocean energy is naturally turning to composite materials because of their perceived noncorrosive properties in the harsh saltwater environment as well as their high specific strength and stiffness. Tidal
turbines are to the forefront due to their reliable and predictable power delivery to the grid and the absence of
overload conditions. A number of different designs of tidal turbines are already at utility scale trials. A lowsolidity, two-bladed turbine, similar to wind turbines, and a high solidity, multi-blade, ducted rotor are presently
undergoing customer testing [1]. Wave energy converters are also under consideration with a number of devices
at full size prototype stage. Glass-fibre reinforced polymers (GFRP) are candidate low-cost materials for the
blades of tidal turbines and the energy collection surfaces of wave devices. It is therefore important to
understand the durability and performance of such materials for these applications. There have been recent
reports of failure in the blades of tidal turbines. The structural properties of GFRP materials depend on
orientation of the fibres, polymer type and fibre/polymer volume fraction. One of the main advantages of fibre
reinforced materials is the ability to align the strong, stiff fibres with the main loads and thereby use the material
to its maximum advantage. There are situations, however, particularly in relation to emerging technologies e.g.
ocean energy, where (i) the loads are not very well understood, or (ii) the loads are complex and multidirectional in nature, for which a class of fibre-reinforced laminates called quasi-isotropic (QI) can be used. The
typical QI layup has equal numbers of fibres at 0, 45, 90, and 135 degrees although many other configurations
are possible. Often QI laminates are used for an entire structure or they can be implemented locally on other
laminate types by adding extra plies of reinforcement around high stress features (e.g. holes). As suggested by
the name, QI laminates can be considered to be isotropic for all in-plane properties (at least for 1st order
approximations). The tensile strength of QI laminates is primarily determined by the volume fraction of glass
fibre (Vf) in the laminate which normally varies between 30 and 70%. The fatigue strength at high stress is also
related to the glass fibre strength, but at high cycles (low stress) the polymer matrix properties become more
important in determining fatigue life [2].
The most common resin used with glass fibre reinforcement is orthophthalic polyester. This material is used
extensively in the pleasure boat industry due to its low cost and ease of use. A resin rich layer (“Gel coat”) of
isophthalic polyester is normally applied to the outer surface of boat hulls to reduce the ingress of water. GFRP
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using these resins are the least durable of the thermosetting resins when immersed in water. After
approximately a year in room temperature water they lose 20% of their bending strength [3] and after 4 years it
has reduced to 70% of their initial value [4]. Accelerated aging in higher temperature water (50° - 65°C )
reduces shear strength by an average 35% [5] and compression after impact by 50% [6]. A number of
investigators have reported hydrolysis (leaching of matrix constituents) from these laminates [4] [5] [7],
postcure is shown to reduce this considerably [8] and improve performance (e.g. retains 83% of strength after 2
years in 30° C water) [9].
Vinyl ester resins absorb less water than the other resins [10] [5]. E-glass/vinyl ester composites maintain their
mechanical properties slightly better than polyester resins and combined with their higher initial performance it
means they enjoy a 32% strength advantage after 2 years in water [9] .
Epoxy resins absorb water at approximately the same rate as other resins but instead of saturating after a few
months they continue to absorb water until they contain almost 2.5% moisture by weight [5]. Epoxy E-glass
composites are shown to lose 8 to 30% of their shear strength after 18 months in room temperature water with
the lower number achieved by post cured laminates[5][10]. The tensile strength of notched epoxy E-glass
composites decreased by 13% after 125 days in room temperature water and by 47% after 42 days in 57° C
water [11].
There are a number of “watch outs” in the literature when aging coupons in water. Void content can have a
large effect on the weight of water absorbed [12] and this may partially account for the warning that percent by
weight of water absorbed is not a good predictor of mechanical property loss [13]. Distilled water is more
aggressive than seawater in penetrating composites [14] and may have different damage mechanisms [5].
Accelerated aging by increasing the temperature of the water is desirable but difficult to calibrate [15] and
becomes increasingly suspect as it nears the Tg of the material.
As regards the fatigue life of GFRP in seawater there are two aspects to be considered. First the effects of
moisture degradation of the material and secondly effects due to fatigue cycling while immersed in water. It is
tempting to assume that fatigue strength reductions will follow the changes in static strength but Talreja [2] has
pointed out that the damage mechanisms are different in fatigue and therefore it is an unreliable assumption.
Unfortunately the data is so sparse a trend cannot be established. The second effect is more marked with a
couple of investigators reporting that cycling while immersed may reduce fatigue life by as much as a decade
[16][17]. It is proposed that the cause is hydrodynamic effects from water in cracks in the laminate opening and
closing.
In this paper results are presented for fatigue of vinyl ester/E-glass and epoxy/E-glass coupons. Based on these
results and results from the literature, the fatigue life of a representative tidal turbine is estimated using stress
and strain data from a finite element model of a tidal turbine under a simplified but realistic loading.
Fatigue degradation of composites was best described by Talreja in 1981 as having three distinct zones where
the mechanisms of failure are very different [18]. Zone 1 is high stress cycling where the strains are high
enough to break the fibres directly and the number of cycles to failure depends on the random accumulation of
fibre breaks at any cross-section reducing the strength of the material below the applied stress. In zone 2 the
matrix cracks under the combination of strain and cycling but these cracks are stopped by the fibres through a
combination of mechanisms. Cracks accumulate and cause some fibre breaks until the damage lowers the
material strength below the applied stress at some (random) cross-section and fracture occurs. In zone 3 the
strain is less than that needed to cause matrix cracking and although there is inevitably some small damage it
does not grow at any appreciable rate and the number of cycles to failure is essentially infinite.
Just as fibre orientation and volume fraction control the static strength of a composite they are also are the
primary determinants of fatigue strength. In fact in many cases fatigue strength is normalised by UTS and
generally shown that zone 2 starts between 100 and 1000 cycles at approximately 80% of UTS and drops to
approx. 25% at over 1 million cycles [19]. The matrix and size (bond promoter) also have an influence on both
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the UTS and fatigue strength with some resins being developed specifically for additional fatigue strength [20]
thereby changing the UTS to fatigue strength relationship slightly (~ 5%). Service temperature will impact both
UTS and fatigue life in equal measure at least for an initial approximation [19]. Unfortunately UTS prediction is
not an exact science but approximations are available [21], testing is much quicker than fatigue testing, and the
equipment and skill needed is much less sophisticated. Other materials related influences are the detrimental
effects of woven fabrics, tightly stitched fabrics and high volume fractions (above 40% for dry fabrics, above
60% for prepreg) [22].
The next set of influences on fatigue life has to do with the nature of the fatigue load experienced by the
material. First of these is the relationship between cyclic amplitude and mean stress. This is usually
represented by constant life lines on a Goodman diagram and by the R ratio found by dividing the minimum
stress in the cycle by the maximum stress. Data from [23] and [22] show that it is a complicated pattern where
CLL's change shape as the number of cycles to failure rise. In particular it is shown that for high cycle fatigue
compressive mean stress is less detrimental and tensile mean stress is more detrimental than would be expected
by the classical triangular Goodman lines. The influence of off-axis loading or normal and shear stresses on
fatigue strength has been extensively studied [24] with shear stresses seen to be more detrimental [25]. Various
models have been proposed and a review [26] shows that a modified Tsai-Hill criterion is promising. The
sequence of load cycles is also shown to be important with random spectrum loading shown to reduce life by
over 50% over more ordered spectra [27]. This is seen as a key deficit of Miner's summation method but so far
no other method explains this phenomena well and work on fatigue damage evolution continues [28][29].
Fatigue testing of coupons using various measurement techniques provides insights into the fatigue behaviour of
GFRP. High frequency cyclic loading (>10 Hz) can cause autogenous heating and early failure [23] so low
frequency testing is necessary. Constant rate of strain application (RSA) testing is recommended and can help
speed up testing at high cycles [19]. Waveform (Triangular, Sinusoidal, of Square wave) has some effect at low
cycles [30] but little effect at high cycles [19]. All fatigue failures in laminated GFRP are preceded by
significant matrix cracking. In fact a characteristic of these materials is that damage spreads throughout the
coupon (at least in straight sided tensile specimens) before becoming localised and causing failure [31]. Matrix
cracking always starts in the most off-axis ply and fatigue matrix cracking starts at lower strains than during
quasi-isotropic testing [32]. These cracks always start at the edge of the coupon [32] and appear to be
significantly suppressed (2 decades) in structures with no free edges [30][33]. Matrix cracking causes an initial
drop in stiffness followed by a further slow decline over most of the fatigue life finishing with a final sharp drop
to failure [34]. Total stiffness loss during this process is on the order of 10 to 20% [35]. Residual strength has a
similar pattern [36] and both phenomena have been used to model damage in composite laminates [37]. In fact
many models have been proposed for composite fatigue [list] but they all require careful application by the
analyst. Fatigue testing of actual components under realistic loadings remains the only way to positively
determine the fatigue life of composite materials.
Despite a vast and fascinating variety of proposed configurations for tidal (or marine current) turbines [38] it
must be conceeded that the standard wind turbine configuration will be the benchmark against which all other
proposals for tidal turbines are measured. Hydrodynamic design of tidal turbine blades can be expected to
follow similar pattern to that of wind turbine blades. Blade element momentum approaches have already been
verified [39] and investigation of cavitation shows that it should not be a problem [40]. Blade element
momentum theory is used for preliminary design of wind turbine rotors [41] following a method suggested by
Glauert using tip loss factors according to Prandtl. Modelling wake rotation improves the accuracy of BEM and
Van Briel has detailed a technique to avoid numerical difficulties near the hub [42]. Detailed design of wind
turbine rotors uses specalised aeroelastic codes [43].
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2. METHOD
This analysis uses a series of linked models to design a tidal turbine blade and predict the life of its composite
structure. The first model is a tidal model which predicts the tidal current speed at any time when given some
local velocities. That water velocity is then used in a hydrodynamic model which outputs the chord, angle with
the rotor plane, and force applied to each section of the turbine blade. A finite element model of the blade is
constructed using these parameters and used to find the maximum strain in the blade. The fatigue model takes
each rotation of the blade explicitly and uses the models previously described to find the maximum strain in the
blade on that cycle. It then takes that maximum strain (and an assumed cyclic component), compares them to an
experimentaly determined Strain-Life curve for the material and obtains a damage fraction for that cycle.
Summation of the damage fractions using Miner’s rule gives an estimate for the life of the tidal turbine blade.
The flowchart shown in Figure 1 depicts the methodology just discussed.
2.1 Tidal Model
Normally there are two high and two low tides of roughly equal magnitude per day with the magnitude varying
by approximately 40% in a repeating 29 day cycle. The highest tides, called spring tides, occur when the sun
and moon are in alignment. This happens twice in each cycle. The lowest tides, called neap tides, also happen
twice per cycle when the moon is at 90° to the sun [1]. Figure 2a shows a typical tidal pattern from the west
coast of Ireland [44]. Tidal currents become magnified in areas where large bodies of water are connected to the
main sea by relatively small inlets. The water speed depends on the local topography, but if the spring and neap
maximum velocities are measured, the full cycle can be approximated by a combination of a semi-diurnal
sinusoid and a fortnightly sinusoidal function [45] [46]. The tidal current velocity at any time t is
𝑉𝑡 = cos(𝜔𝑑 𝑡) [𝑣𝑎𝑣𝑒 + 𝑣𝑎𝑙𝑡 cos(𝜔𝑚 𝑡)]
(1)
where 𝑣𝑎𝑣𝑒 is the average of the peak tidal velocities, 𝑣𝑎𝑙𝑡 is half the range of peak tidal velocities, 𝜔𝑑 is the
angular frequency of the tides, and 𝜔𝑚 is the angular frequency of the spring-neap (14.7 day) cycle. Figure 2b
shows the pattern given by Equation 1.
2.2 Hydrodynamic Model
The tidal current flows over the turbine blades creating lift and drag which turn the blades and power the
turbine. The lift and drag forces can be estimated to a first order approximation using a stream tube momentum
model [47]. The model, as shown in Figure 3, assumes a series of isolated concentric tubes within which
momentum is conserved as it is transferred from the water to the blade. For steady state operation the fluid
forces on the blades inside any stream tube must equal the momentum lost from that stream tube
2𝑀̇
𝐹𝐴 = ( ) (𝑉𝑡 − 𝑈𝑑 (𝑅))
𝑁
(2)
where 𝐹𝐴 is the sum of the axial components of the lift and drag forces on the blade element inside the tube, N is
the number of blades on the turbine and 𝑀̇ is the mass flow rate through the tube, 𝑉𝑡 is the tidal current velocity
and 𝑈𝑑 is the axial water velocity at the rotor disk. The factor of 2 appears in the equation because as [48]
shows half the total reduction in velocity occurs upstream of the turbine blades. A similar argument pertains to
the relationship between torque and angular momentum of the fluid. Within each stream tube the tangential
components of the lift and drag forces sum to give a torque producing force and this imparts angular momentum
to the blade. This angular momentum is balanced by an angular momentum of the fluid in the opposite
direction, causing wake rotation. Transformation to a rotating coordinate system and making the assumption
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that the relative resultant water velocities are constant allows generation of equations [42] giving axial and
rotational velocity at the disk, as follows:
𝑈𝑑 =
𝑉𝑡
√1 + 𝛾 2 + 𝜁 − 𝛾√(1 + 𝛾 2 − 𝜁 2 )
𝜋
𝑉𝑑 = 𝑈𝑑
(3)
√1 + 𝛾 2 − 𝜁 2 − 𝛾
1−𝜁
(4)
where 𝑈𝑑 is the axial velocity in a stream tube at the rotor disk, 𝑉𝑑 is the tangential velocity of the fluid in a
stream tube at the rotor disk, 𝜁 is the fraction of axial velocity remaining at the downstream exit of the stream
tube, and 𝛾 is the local speed ratio given by
𝛾=
𝜔𝑏 𝑅
𝑉𝑡
(5)
where 𝜔𝑏 is the angular velocity of the blade, R is the radius, and 𝑉𝑡 is the freestream velocity of the fluid. The
blade also has a tangential velocity 𝑉𝑏 at the stream tube due to its angular velocity:
𝑉𝑏 = 𝜔𝑏 𝑅
(6)
The apparent or relative velocity seen by the blade is then:
(7)
𝑉𝑟 = √𝑈𝑑 2 + (𝑉𝑑 + 𝑉𝑏 )2
and the angle between the relative velocity and the plane of the rotor is given by:
𝜃 = tan−1
𝑈𝑑
𝑉𝑑 + 𝑉𝑏
(8)
The lift and drag forces generated by a stream tube on the blade section inside it are thus given by:
1
(9)
1
(10)
𝐿 = 2𝐶𝐿 𝑉𝑟 2 𝜌𝑆∆𝑅
𝐷 = 2𝐶𝐷 𝑉𝑟 2 𝜌𝑆∆𝑅
where 𝐶𝐿 and 𝐶𝐷 are the coefficients of lift and drag for the aerofoil selected, 𝜌 is the density of the fluid, S is
the chord length of the blade at the stream tube radius and ∆𝑅 is the radial thickness of the stream tube. The lift
force is always perpendicular to the fluid velocity and the drag force always parallel. These are translated into
axial and tangential forces by
𝐹𝐴 = 𝐿𝑐𝑜𝑠𝜃 + 𝐷𝑠𝑖𝑛𝜃
(11)
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𝐹𝐶 = 𝐿𝑠𝑖𝑛𝜃 + 𝐷𝑐𝑜𝑠𝜃
(12)
where 𝐹𝐴 is the axial (thrust) force acting on the blade by that stream tube and 𝐹𝐶 is the tangential (torque)
force. For maximum power output:
2
𝑈𝑑 = 𝑉𝑡
3
(13)
per the well-known Betz limit. The inputs to the hydrodynamic program are; blade length and number of blades,
number of streamtubes to be used in the calculations, tip speed ratio, lift and drag coefficients of the aerofoil,
optimum angle of attack for the aerofoil, water velocity and density, and finally a target for 𝜁 which is fraction
of velocity remaining far downstream. The program then calculates all the parameters mentioned above and
adjusts the chord length until the momentum balance is achieved. The output from the program at each radial
increment is; chord length, angle the aerofoil makes with the rotor plane, axial force and tangential force on the
blade at that radial increment.
2.3 Structural Model
In common with modern wind turbines there is a significant structural challenge in reacting the loads placed on
the turbine blades within the slender aerofoil shape of the turbine blade. A set of aerofoil shapes with relatively
thick section (24%) compared to chord length have been developed e.g. NACA 63-421, RISO-A1-24 (see
Figure 6) to achieve good lift and drag performance while maximizing the cross section area moment of inertia
allowing for good structural characteristics [49]. The challenges associated with upscaling of wind turbines
blades, e.g. see Garvey [50], are significantly more pronounced in the context of the increased fluid density
associated with tidal turbine blades. Consequently, it can be anticipated that upscaling of tidal turbines will
present significantly larger challenges. Preliminary calculations for the present paper with a simplified aerofoil
shape (box beam with triangles front and back), and the material chosen for the turbine blade (i.e. quasiisotropic GFRP), have indicated, that for turbine blades longer than 10 m, the bending stresses become
prohibitively large, with respect to (fatigue) failure, due to the significant dependence of hydrodynamic loading
on blade length. This analysis is summarised in Table 1.
Consequently, the present work is focussed on the fatigue life of a smaller "low cost" turbine. This low cost
version is a 5 m radius, 3-bladed, downstream, free-yaw turbine, which should produce approximately 250 kW
at 2.5 m/s tidal current velocity. This configuration eliminates expensive pitch and yaw systems and allows for a
simple robust construction. A shell element model of the outer 3.5 m of the turbine blade has been constructed
in the ABAQUS finite element program as shown in Figure 5. The blade chord length is 750 mm at the tip and
makes an angle of 4 degrees with the plane of the rotor. It tapers and twists to 1250 mm and 20 degrees at 1.5 m
radius. The aerofoil shape has been simplified in the structural model, representing the smooth aerofoil curved
surface, shown in Figure 6, by a piecewise linear equivalent (Figure 7) but it maintains a 24% section thickness.
Following the practice in the wind turbine industry, e.g. see [51], two shear webs have been inserted into the
aerofoil shape creating a box section which becomes the structural core of the blade. The top caps of this box
are 70 mm thick laminates, the shear webs are 40 mm thick, and the nose and tail fairings are 25 mm thick. In
the finite element model the panels of the blade are modelled as shell elements with QI material properties from
standard laminate analysis [52]. The values chosen here are shown Table 1. The laminates have constant
thickness along the length of the blade. High stress locations are modelled with individual plies near the
surface. Material properties for the individual plies are calculated from the rule of mixtures and the Halpin-Tsai
equations [53]. All elements are 4-node doubly curved shell elements with reduced integration.
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EFFECT OF THE CONTROL SYSTEM
Control systems can have a significant effect on the loads experienced by a tidal turbine by reducing the
power absorbed by the turbine during high water velocity. However they are expensive to implement and errors
or failures can cause catastropic damage to the turbine structure. Wind turbine control system have evolved
from simple spring loaded systems to sophisticated full span pitch control blades and they continue to improve.
Some of the reason for this is that wind turbines operate in an environment of large changes in power density.
Most machines work with average windspeeds of approximately 8.5 m/s, they must continue to operate up into
a 25 m/s wind which could provide over 25 times as much power, and it is required to survive, when stopped, in
40 m/s winds which are over 100 times more powerful than 8.5 m/s. In contrast a tidal turbine has much less
range of power densities to deal with, for example a fast tidal current would have 2.0 m/s average with 4.0 m/s
maximum which has only 8 times difference in power available. It may be therefore that simpler control
systems are appropriate for tidal turbines. Figure 8 shows the power curve and thrust moment curve for a pitch
regulated tidal turbine where the power is regulated at 530 kW. Figure 9 shows a similar graph for a stall
regulated constant speed turbine which makes up to 630 kW in a 4 m/s tidal flow. At the tidal pattern chosen for
this study these turbines would have similar energy output in a year. One of the questions this study will
attempt to answer is how much heavier will the stall regulated blade have to be in order to have the same life
expectancy.
2.4 Experimental Method
Quasi-isotropic laminates have been manufactured using the VARTM (Vacuum Assisted Resin Transfer
Moulding) process. Biaxial stitched glass-fibre mat (0°-300 g/m2, 90°-300 g/m2) was cut to give ±45° material
and 0°/90° material and then stacked to create a [(45\135\90\0)2]s laminate. Either vinyl ester or epoxy resins
were introduced under vacuum to complete the laminate (see Figure 10). After a room temperature cure for 48
hours, the laminates were oven cured at 80° C for 3 to 5 hours. Volume fractions of approximately 50% were
achieved at an average thickness of 3.75 mm. The laminates were cut into 25 x 250 mm coupons using a water
cooled diamond abrasive disk.
Fatigue tests were performed with an Instron 8500 test machine and 8800 controller applying a sinusoidal force
in tension-tension mode (R = 0.1) between 5 and 12 Hz. The frequency is decreased to maintain a constant rate
of strain application as the strain level increases [19]. A fan was used to cool the coupon during testing and a
radiation thermometer measured less than 10° C temperature rise in surface temperature during the highest
stress cycling test. Five coupons were tested at each of four separate stress levels. A relationship between
maximum initial strain (𝜖𝑚𝑎𝑥,𝑖 ) and fatigue life of the form
𝜖𝑚𝑎𝑥,𝑖 = 𝐴𝑁𝑓−𝐵
(14)
where 𝑁𝑓 is the number of cycles to failure, and A and B are constants, is found to be a good fit for the data (as
shown below) so that it can be used in the fatigue model.
2.5 Fatigue Model
The fatigue model focuses on the highest tensile strain in the blade, which is predominantly attributed to
bending-induced strain. Each cycle of the tide causes a slow increase and then a decrease in the maximum strain
on the blade – this is a cycle in itself but there are only 2 per day. Simultaneously the blade experiences a cyclic
load for each revolution of the machine, caused by the blocking (‘shadow’) effect of the support tower as shown
in Figure 4. The tower causes a reduction in the water velocity downstream of itself and consequently a loss of
lift on the blade, leading to reduced bending moment on the blade for a short time (see Figure 12). The
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magnitude of this brief reduction in bending moment depends on the geometry of the particular turbine.
Obviously if the tower blocks the flow completely, the drop in bending moment, and hence strain, approaches
100%. Test data on a downwind wind turbine shows a 30% drop in bending moment [48]. Wave interaction can
also lead to fluctuations in the load on tidal turbine blades. Experiment with scaled models of tidal turbines in a
wave tank have found flapwise bending moment amplitudes of 50% [54]. For the present study two cases are
considered, reductions of either 50% or 90% of the bending moment in the tidal turbine blade. This corresponds
to a fatigue loading R-ratio (𝜀𝑚𝑖𝑛 /𝜀𝑚𝑎𝑥 ) of 0.5 and 0.9 respectively.
There is no generally accepted method for dealing with the effect of mean stress in fatigue of composites, i.e.
for inferring the ε - N curves from one (test) R-ratio to a different R-ratio. The approach adopted here, to infer
the R = -1 and R = 0.5 ε - N data from the (measured) R = 0.1 data, is based on that described in [56]. This is
based on the following assumed behaviour for constant life diagrams (CLD) as illustrated in Figure 11:
1. For -1 ≤ R ≤ 0.5, the constant life lines are assumed to be parallel between R = -1 and R = 0.5, based on
experimental observations, e.g. [57].
2. The Nf = 5000 points for each of R = 0.5, R = 0.1 and R = -1 all lie on a straight line which also passes
through the material UTS (equivalent strain, in this case).
The present work is only concerned with R ≤ 0.5.
[For a constant tip speed ratio, the bending moment (and strain) in the blade is related to the square of water
velocity. Therefore the maximum strain at any time j is found from the following equation:
𝟐
𝒗𝒋
𝜺𝒎𝒂𝒙,𝒋 = 𝜺𝒎𝒂𝒙, 𝒔𝒑 (
)
𝒗𝒎𝒂𝒙,𝒔𝒑
(15)
where 𝑣𝑗 is the tidal current velocity (from Equation 1) at time j, as predicted by the tidal model, 𝑣𝑚𝑎𝑥,𝑠𝑝 is the
maximum velocity on the spring tide, and 𝜀𝑚𝑎𝑥, 𝑠𝑝 is the maximum strain on the spring tide.] This section is not
correct any more and in the model I use equations to for bending moment to interpolate the strain levels – will
fix later.
The fatigue model has two components, the first looks at the damage caused by the tidal cycles themselves as
the turbine strains increase in parallel with the increase in water velocity as the tide comes in and then dies away
to zero as the tide turns. The turbine yaws into position for the outgoing tide and a similar cycle is repeated. In
this section the fatigue model steps through time in increments that correspond to the tidal period. It finds the
tidal velocity from Equation 1 and uses Equation 16 to find the maximum strain in the blade during peak tidal
flow. The number of cycles before failure in a coupon at that strain is found from strain-life equation for R = 0
and used in Equation 17 to give the damage fraction for each tidal cycle.
The second section in the fatigue model looks at the damage caused by the cycles due to tower shadow. The
fatigue model steps through time in increments of the time required for one revolution of the turbine. Again it
finds the tidal velocity from Equation 1 and uses Equation 16 to find the maximum strain in the blade during
that revolution. Depending on which case is being investigated (R = 0.1 or R = 0.5) it uses Equation 15 and the
appropriate coefficients to find the number of cycles to failure at that load level for use in Equation 17. The
model then increments to the next revolution and repeats the process. In this way the damage fractions are
summed by Equation 17 to find the 7-day damage and hence the turbine life, using a Miner’s rule approach, as
follows:
𝑁7−𝑑𝑎𝑦
𝐷7−𝑑𝑎𝑦
𝑁7−𝑑𝑎𝑦
1
1
= ∑
+ ∑
𝑁𝑓,𝑘
𝑁𝑓,𝑗
𝑘,𝑡𝑖𝑑𝑒
(16)
𝑗,𝑟𝑒𝑣
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where N7-day is the total number of time increments at which damage is calculated, Nf,j is the number of cycles to
failure (calculated from Equation 15, incorporating the mean stress effect) at the strain level in a given time
increment, k is the increment of tidal cycles, and j is the increment of cycles due to revolutions of the turbine.
3. RESULTS
Results are shown in Table 1 for the preliminary investigation into possible blade lengths. This used bending
moments from the hydrodynamic model and an estimated moment of inertia for the chosen aerofoil section.
Comparing the bending stress to the stress which is estimated to equate to 20 year fatigue life shows that a 10 m
blade from QI epoxy / E-glass laminates is not feasible in a 4 m/s tidal current. (This was true for constant tip
speed ratio blades but it SR and PR blades have less moment so it may not be true, or it may only be true only if
we include reliability offsets – this would take time to analyse and explain – so I may have to leave this section
out.)
Figure 14 shows the distributions of tangential and thrust forces versus radial distance along the 5 m blade
(from hub), as predicted by the hydrodynamic (stream-tube) model described above for a 2.6 m/s tidal velocity.
Clearly, the thrust force, which increases linearly with increasing radius from about 0.7 kN to about 2.3 kN at
the extreme blade radius, is significantly more than the (power-generating) tangential force which increases
asymptotically with radius from about 320 N at a small radius to a value of about 410 N at the extreme blade
radius. These forces cause a flapwise bending moment of 150 kN.m and an edgewise bending moment of 35.7
kN.m at 1.5 m radius from the rotor centre. The model uses 45 streamtubes of 78 mm “wall thickness” out along
the blade, and assumes that the water in each of these tubes is slowed to 1/3 its final velocity. It uses a
coefficient of lift of 1.0 for the airfoil, a lift to drag ratio of 70, 16.75 rpm, and produces 330 kW.
Figure 16 shows the deflected shape of the blade under these applied forces, as predicted by the FE model
described above. The forces are applied as surface traction distributions (in the relevant directions) on the spar
caps of the blade. This is based on the assumption that the resultant forces act through the ¼ chord point ( ¼ of
the chord length back from the leading edge of the aerofoil) of each blade section [48]. The tip deflects axially
approximately 132 mm under these loads which is less than the blade thickness at the tip. This amount of
deflection will not introduce any significant error into either the structural or hydrodynamic calculations. The
highest stresses and strains are predicted near the hub in the caps of the box section spar which form the main
structural member of the blade. These are primarily caused by the large bending moments due to the thrust
force. Bending strains are at their maximum on the outer surface but the 3 outermost plies are at ±45° and 90°
which reduces their fibre strains. The 4th outermost ply is at 0° and the fibres are aligned with the main bending
strains. The maximum fibre strains are predicted in this ply, as shown in Figure 17.
Figure 18 shows the strain-life fatigue test results for the epoxy/E-glass and vinyl ester/E-glass materials along
with the corresponding power law curve fits, as per Equation 15. The identified fatigue strain-life power-law
constants for the two materials are given in Table 3, along with the inferred R = 0.5 constants, based on the
mean stress diagram procedure described above. The superior performance of the epoxy resin over the vinyl
ester resin is obvious. It is observed during the testing that epoxy appears more tolerant of the cracks and minor
delaminations that appear at the edges of the coupon during testing. Certainly the epoxy specimens are more
obviously damaged before they finally fail as can be seen in Figure 20.
Figure 10 shows the predicted relationships between maximum fibre strains in the turbine blade and life to
failure, based on the data of Table 2 and the fatigue life methodology described above. Clearly, the combination
of relatively flat -N curve for the material and the cyclic load spectrum modelled here leads to a high degree of
sensitivity of predicted fatigue life to predicted strain level. Just 13% (epoxy) or 16% (vinyl ester) increase in
strain levels will decrease life from 20 to 5 years.
9
Copyright © 2011 by ASME
The advantage of this flat sensitivity curve is that when maximum strains are kept below the critical levels a
long life is assured. If the 5m tidal turbine modelled here is in a tidal zone with a maximum tidal current
velocity of 4.0 m/s, the combined hydrodynamic and structural FE methodology described above predicts a
maximum strain of 0.61%. If the neap tide velocity in that zone is 2.4 m/s and the R ratio is 0.5 as discussed
then the fatigue model described gives a predicted fatigue life of 2,500 years for epoxy/E-glass. A change in
stress ratio of the cyclic load will have a significant effect on the fatigue life of the turbine blades. If the tower
shadow effect discussed earlier changes from a 50% dip in load to a 90% dip in load the stress ratio changes
from 0.5 to 0.1. The maximum strain in the R = 0.1 case must be 19% less if the blade is to have the same life as
in the R = 0.5 case. The other factor in the turbine life is the material choice. Vinyl ester / E-glass must have
approximately 25% less strain than epoxy / E-glass to achieve the same life.
Figure 19 shows energy capture and damage for the different control schemes. This graph is obtained by
“binning” the data [57]. For each rotation of the turbine the data for energy created during that rotation, and
damage sustained during that rotation, are added to a series of bins based on water velocity. At the end of the
period the sum of the data in each bin is reported. As mentioned earlier the stall characteristics and the pitch
regulating point of the corresponding blades were chosen to give the same energy capture over the 20 year
design life. The graph also shows the pattern of damage accumulation over the life of the blade. The stall
regulated blade sustains a lot of its damage at high water velocities and this does cause proportionaly more
damage than that sustained by the pitch regulated blade. A blade that survives 20 years on the pitch regulated
machine will only survive 12.8 years on the stall regulated machine. On the other hand, if the laminates in the
spar cap of the blade are increased by just 10% it would survive 22 years on the stall regulated machine.
If the maximum or average speeds at the turbine site do not match the design speed of the turbine it can have
significant impacts on energy production or life of a stall regulated turbine. A 10% decrease in the pattern of
tidal flows will reduce energy production per year by 20%, whereas a 10% increase in tidal speed will reduce
life from 20 to 12.1 years. A pitch regulated turbine would not suffer nearly so badly in this situation. An
increase in water velocity will not decrease life because the blades will feather at maximum power either way.
There will be some loss in energy produced because the average will be lower but looking at the bins data
(Figure 19) it can be seen that only 1/4 of the energy is produced before the pitch regulation point and will be
effected by the loss in speed, above this point the turbine will make the same power either way.
4. CONCLUSION
A combined hydrodynamic and structural fatigue life assessment methodology for tidal turbine blades,
based on a stream tube model for determination of hydrodynamic loads and an FE model of a composite
material blade for the fatigue stress and strain history prediction, is presented. The results show that the fatigue
life of this design of tidal turbine is sensitive to the maximum strain level experienced. Epoxy / E-glass is
approximately 25% more fatigue resistant than vinyl ester / E-glass in this application. These materials are also
both sensitive to the stress ratio of the cycles experienced by the material with approximately 20% less
resistance to fatigue when they undergo R = 0.1 cycles than when they experience R = 0.5 cycles. Details that
have not been considered in this analysis (e.g. joints, stress concentration at holes.) will need to be incorporated
in future developments of this methodology for more realistic lifetime analysis and design. Future work will
also need to address more detailed modelling of the material, e.g. micromechanical models or laminate
10
Copyright © 2011 by ASME
analyses, to furnish better mechanistic understanding of the failure modes, and, in particular, modelling of
individual plies with associated orientations, e.g. other than quasi-isotropic laminates.
5. ACKNOWLEDGEMENTS
The author wishes to thank ÉireComposites Teo. for manufacture of the laminate specimens, and CTL
Tástáil Teo. for preparation of the tensile coupons.
11
Copyright © 2011 by ASME
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Copyright © 2011 by ASME
FIGURES
Figure 1
Flowchart of fatigue life methodology
15
Copyright © 2011 by ASME
(a) tide height data
7 day period
5
Water velocity (m/s)
2.5
0
-2.5
-5
0
5
9
14
Days
(b) sinusoidal model output
Figure 2 (a) Typical tidal pattern around Ireland [44], and (b) sinusoidal model for water velocity
16
Copyright © 2011 by ASME
Figure 3 Stream tube model
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Copyright © 2011 by ASME
Figure 4 Tower shadow effect
Figure 5 Finite Element Model
18
Copyright © 2011 by ASME
Figure 6 Example of thick section aerofoil
Figure 7 Simplified aerofoil shape used for analysis
19
Copyright © 2011 by ASME
600
300
Thrust moment (PR)
400
200
300
150
200
100
100
50
-
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Water Velocity (m/s)
Figure 8 Power and Root bending moment for pitch regulating tidal turbine
700
400
600
350
Power
Thrust mom (16 rpm)
250
400
200
300
150
200
Thrust Moment (kN.m)
300
500
Power (kW)
Power (kW)
250
Power (PR)
Thrust moment (kN.m)
500
100
100
50
-
0
1
2
3
4
5
Water Velocity (m/s)
Figure 9 Power and Root bending moment for stall regulated constant speed turbine
20
Copyright © 2011 by ASME
Resin
introduced
here
Vacuum
applied
here
Resin flow front
Figure 10 Laminates being manufactured by Vacuum Assisted Resin Transfer Moulding (VARTM) process
21
Copyright © 2011 by ASME
Figure 11 Schematic for constant life extrapolation from R = 0.1 test data to equivalent R = 0.5 data.
22
Copyright © 2011 by ASME
Unimpeded
Flow
0.6
0.5
ε
max
(%)
0.4
0.3
0.2
Tower
Shadow
0.1
0
0
2
4
6
8
10
12
Time (hr)
Figure 12 Schematic of effect of tower shadow on maximum strain in the turbine blade
23
Copyright © 2011 by ASME
1.2
20
0.8
15
10
0.4
5
-
Chord Length (m)
Angle (Degrees)
25
0.0
1
3
5
Radius (m)
Figure 13 Blade angle and chord output from Hydrodynamic model
Forces on each blade section (kN)
2.5
FA
2.0
1.5
1.0
FC
0.5
0.0
1
2
3
4
5
Radius (m)
Figure 14 Axial (FA) and tangential (FC) forces from hydrodynamic model at 2.5 m/s
Figure 15 Loads on blade at 4.0 m/s tidal velocity
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Copyright © 2011 by ASME
Figure 16 Undeformed and deformed shape of blade at full load (displacements magnified by 5)
0.7
Strain in outermost 0° ply (%)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.0
2.0
3.0
4.0
5.0
Radius (m)
Figure 17 Fibre strain in outermost 0° ply
25
Copyright © 2011 by ASME
2
QI Epoxy / E-glass
QI Vinyl ester / E-glass
Maximum strain (%)
1.5
1
0.5
0
1.00E+02
1.00E+03 1.00E+04
1 x 102
1 x 104 1.00E+05 1.00E+06
1 x 106 1.00E+07 1.00E+08
1 x 108
Number of cycles to fracture
Figure 18 Test results for QI laminates (R = 0.1)
2,500
0.2
0.18
Energy (SR)
2,000
0.16
Damage (PR)
0.14
Damage (SR)
1,500
0.12
0.1
1,000
0.08
Damage fraction
Energy capture over 20 yr. (MW.hr)
Energy (PR)
0.06
500
0.04
0.02
-
0
0
1
2
3
4
5
Water Velocity (0.1 m/s Bins)
Figure 19 Energy capture compare to damage for PR and SR blades
26
Copyright © 2011 by ASME
Figure 20 Post fatigue-test specimens of Vinyl ester (left) and Epoxy (right)
1.1
Maximum strain (%)
1.0
Epoxy R 0.5
0.9
0.8
Epoxy R 0.1
0.7
V Ester R 0.5
0.6
V Ester R 0.1
0.5
0.5
0
5
10
15
20
25
Time to failure (years)
Fig. 10 Fatigue life versus maximum strain for Epoxy / E-glass and Vinyl ester / E-glass laminates.
Table 1 Effect of blade length on bending stress
Blade length (m)
Chord near root
(mm)
Flapwise
moment (kN.m)
Bending stress
(MPa)
2.5
5
10
12.5
593
1,186
2,372
2,965
44
349
2,792
5,453
83
110
175
208
27
Factor of safety
on 20 year
stress
2.1
1.6
1.0
0.9
Copyright © 2011 by ASME
Table 2 Glass fibre/epoxy material properties
Inputs
Vf
Ef
νf
Em
νm
50%
72.4 GPa
0.22
3.5 GPa
0.35
Single
unidirectional
ply properties
E1 38 GPa
E2 11.6 GPa
G12 3.5 GPa
ν12 0.285
Quasi-isotropic
laminate
[(45\135\90\0)2]s
Ex, Ey 19.3 GPa
Gxy
7.2 GPa
νxy
0.330
Table 3. Constants for power law fit to fatigue data
Material
Epoxy / E-glass R = 0.1
Epoxy / E-glass R = 0.5
Vinyl ester / E-glass R = 0.1
Vinyl ester / E-glass R = 0.5
Coefficient
(A)
0.02830
0.03507
0.02908
0.03704
28
Exponent
(B)
0.0863
0.0863
0.1063
0.1063
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